Modelling Seashells, Part 2: An Exercise in Abstraction.

This week I describe an artistic exploration I went on after modeling as realistic looking of a seashell as I could using Rhino and Grasshopper (described here). That model was a surface defined by two different curves that were replicated, at increasingly smaller scales, around a logarithmic spiral. Once I had done this, I decided to experiment. I wanted

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Knitting and Printing the Figure-8 Klein Bottle

This week I’ll describe one strategy for representing 4-dimensional objects in 3-dimensions, using both modern and traditional media. While more than three spatial dimensions is a foreign concept to most people, Mathematicians have been studying theoretical objects in four dimensions and more for over a century. (Some contemporary Mathematicians even think about infinite-dimensional things, whatever that means!).

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Modelling Seashells

Anyone who has ever seen my work should have expected that sooner or later I would write a post (or two or three) about seashells…. There are many places in nature where there appear to be mathematical laws at play. For example, pinecones exhibit the mathematical phenomenon of phyllotaxis, tree branching can be modeled with various fractal-generating

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A Plurality of Polyhedra

A little over a year ago (February, 2015) I was contacted by Los Angles artist Clare Graham about making some models. He had become interested in the illustrations of polyhedra in the 1509 book De Divina Proportione, by Luca Pacioli. What’s significant about these  illustrations is that they were done from woodcuts by Leonardo da

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